Christophe LETELLIER
06/01/2018

Kensuke Ikeda proposed a model of a passive optical resonator system [1]. When the system is an optical bistable resonator, Ikeda and Kenji Matsumoto showed that the dynamics can be reproduced with the single delay differential equation [2]

For *μ* = 16 and *x*_{0} = *π*/3, *δ**t* = 0.002 and *x*(0)=2.5, the chaotic attractor shown in Fig. 1 is obtained. These parameter values were obtained by looking for a simple attractor starting from those provided by Voos & Kurths [3].

**Fig. 1. A low-dimensional chaotic attractor produced by the Ikeda DDE.**

[1] **K. Ikeda**, Multiple-valued stationary state and its instability of the transmitted light by a ring cavity system, *Optics Communications*, **30** (2), 257-261, 1979.

[2] **K. Ikeda & K. Matsumoto**, High-dimensional chaotic behavior in systems with time-delayed feedback, *Physica D*, **29** (1-2), 223-235, 1987.

[3] **H. Voss & J. Kurths**, Reconstruction of nonlinear time-delayed feedback models from optical data, *Chaos, Solitons & Fractals*, **10** (4–5), 805-809, 1999.